A fossilized insect wing from the species Stephanotypus schneideri
and it is about 300 million years old. The wing is about 7.5 inches (19
centimeters long), substantially smaller than the largest fossil insect
(Meganeuropsis permiana, about 33 cm long). Superimposed on the fossil
is a drawing of the largest Cenozoic insect (it's about 12 million years
old), Epiaeschna lucida, which comes in at 2.6 inches (6.7 cm) long, similar
to modern insects. (Photo: Wolfgang Zessin and Matthew Clapham)

What happened to giant insects that ruled the skies of ancient Earth?
Studies by Matthew Clapham of University of California at Santa Cruz and
colleagues showed that insects gradually get smaller and smaller as dinosaurs
evolved flight and took to the skies as birds:

Millions of years ago, oversized insects like griffinflies boasting
wingspans comparable to today's hawks scuttled across (and fluttered
above) the planet. But why these jumbo jets of the insect world shrunk
to modern size has remained a mystery, until now.

Turns out, as dinosaurs evolved flight and eventually took to the
skies as birds, they beat down the huge insects already living there,
effectively putting a cap on insect size through predation and competition
in the prehistoric skies, as birds developed into sophisticated flying
machines.

I don't know that this "remained a mystery, until now" - an alternate (and I think more plausible) theory is that the higher oxygen content of the atmosphere in prehistoric times allowed for larger insects: http://insects.about.com/od/evolution/f/Why-Prehistoric-Insects-Were-So-Big.htm

@GoodGuyGreg - higher oxygen level was discussed at the article. Basically, as oxygen level dropped, insects also became smaller ... to a point. It was actually the evolution of birds that finished them off.